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We study theoretically the electron spin noise in quantum dots undernon-equilibrium conditions caused by the pumping by a train of circularlypolarized optical pulses. In such a situation, the nuclear spins are known toadjust in such a way, that the electron spin precession frequencies becomemultiples of the pump pulse repetition frequency. This so called phasesynchronization effect was uncovered in [Science {\bf 317}, 1896 (2007)] andtermed nuclei-induced frequency focusing of electron spin coherence. Using theclassical approach to the central spin model we evaluate the nuclear spindistribution function and the electron spin noise spectrum. We show that theelectron spin noise spectrum consists of sharp peaks corresponding to the phasesynchronization conditions and directly reveal the distribution of the nuclearspins. We discuss the effects of nuclear spin relaxation after the pumping isover and analyze the corresponding evolution of nuclear spin distributions andelectron spin noise spectra.

Electron Spin Noise under the Conditions of Nuclei Induced Frequency Focusing